Target and focus your letter: You are applying to companies that did not propose a job. They don't expect your letter. Therefore, you need to work better your cover letter, in order to explain them why they should consider hiring you, even though they did not think they needed you. This is thus not a mass mailing. If you would send 50 letters responding to some job ads, for an unsollicited candidature you shoud focus on 5. customize them, and spend time making them attractive. You also need to find out to whom the letter is dedicated to (marketing director, or product manager, try to find the chart of the company).

The reason why: Why are you proposing your services? Why did you decide to leave your job? Why do you want to work for this company? Explain the reasons why you are sending your candidature.

What can I bring in? My expertise, my experience, my network, you need to explain the main reasons why you are a great addition for the company.

The tune/style: You need to show your determination off. You need to create empathy. I want to work for you and I already know you. You need to find out about the company: You know it as much as if you'd work for them. Also, in order to affirm the quality of your candidature, feel free to use a nice paper.

Show that you are taking a risk. You must show that you are taking some risks and you are ready to be challenged. You can explain that you are taking some risks, and that you accept it.

The availability: Instead of telling you are available right away, say that you will be available in a month or three. Most of the time, people says they are ready right away, but hiring staffs don't like losers.

What's the next step: When do we get in contact.

Conclusion: The results of such an approach are not as good as the ones resulting from responding to ads. But don't give up! When it works, it is such a great feeling, because you would have picked the company and the position that you wanted to get.